Resumen de Lattice theory and metric geometry
Horst Struve, Rolf Struve
K. Menger and G. Birkhoff recognized 70 years ago that lattice theory provides a framework for the development of incidence geometry (affine and projective geometry). We show in this article that lattice theory also provides a framework for the development of metric geometry (including the euclidean and classical non-euclidean geometries which were first discovered by A. Cayley and F. Klein). To this end we introduce and study the concept of a Cayley�Klein lattice. A detailed investigation of the groups of automorphisms and an algebraic characterization of Cayley�Klein lattices are included.
